The present invention is related to the use of a fractal pattern for progressive transmission of an existing image. More specifically, the present invention is related to the use of a fractal pattern for progressive transmission of an existing image where the fractal pattern renders larger shapes in samples of the pattern as progressively smaller shapes which cover the larger shapes until the larger shapes become represented by smaller shapes each occupying exactly one pixel.
Other techniques exist that use a fractal pattern for progressive transmission of an existing image, such as is taught by Shapiro (U.S. Pat. No. 5,321,776), incorporated by reference herein.
But when the image is being generated procedurally by point sampling, the problem to be solved is different. In this case, the only query that such the algorithm can make at any given moment is xe2x80x9cwhat is the value of the image at a given pixel (i,j)?xe2x80x9d It is this latter problem that the present invention addresses.
A very simple approach would be to first scan the image in a coarse grid, computing every 2Nxc3x972N pixels, and displaying the result as a set of squares of size 2Nxc3x972N, and then to successively halve the grid size until a full-resolution image is displayed. A deficiency with this approach is that it requires computing the value at some pixels many times, which leads to a loss of computational efficiency. In particular, this approach more than 5/4 as many samples as an optimally efficient technique.
Alternatively, the already-computed values could be stored in a table, and reused to create the fine grid. A deficiency with this approach is that it requires either a large amount of intermediate storage for this table, or else the ability to read from the display device colors that have already been written to it.
The present invention suffers from neither of the above deficiencies. It is optimally efficient, requiring only one computation per pixel. In addition, the invention has the advantage that the developing pattern does not appear as a regular grid, but rather as a varying impressionistic pattern that is much more visually pleasing to the viewer, and much less visually distracting, than a simple square grid would be.
The present invention pertains to a method for producing an image. The method comprises the steps of forming a procedural representation of the image. Then there is the step of taking samples of the image. Next there is the step of rendering larger shapes in the samples as progressively smaller shapes which cover the larger shapes until the larger shapes become represented by smaller shapes each occupying exactly one pixel, wherein the time it takes to render each smaller shape is essentially the same.
The present invention pertains to an apparatus for producing an image. The apparatus comprises a computer. The apparatus comprises a memory connected to the computer. The apparatus comprises computer display connected to the computer. The apparatus comprises a pointer device connected to the computer. The apparatus comprises a mechanism for taking samples of the image and rendering larger shapes in the samples of the image as progressively smaller shapes which cover the larger shapes until the larger shapes become represented by smaller shapes each occupying exactly one pixel, wherein the time it takes to render each smaller shape is essentially the same. The taking mechanism is disposed in the memory.